I looked at the pic & it looks like normal 2x2 ribbing to me. Maybe they even mean literal double knitting (there's a vid on this site under advanced techniques) to make it double thick... Not sure, though. Sorry for all the non-help.

Yep, went to scope out the pattern n I am thinking that double knitting is referring to the yarn itself (same as wilds theory), I also think that something was lost in translation when dd transcribed the directions from mum. So I am thinking that that particular phrase isn't really sposed to be there.
It should read:
Cast on 40 sts, knit 2x2 rib for blankety blank amount of inches....